Understanding Scalar Topology Using Contour Tree

Adi Chandra Sekhar

Prasad V Potluri Siddhartha Institute Of Technology, Vijayawada, Andhra Pradesh 520 007

Dr. Amit Chattopadhyay

International Institute of Information Technology-Bengaluru, Bengaluru, Karnataka 560100.

Abstract

Scalar data is used in different applications like geographical information systems, in medical imaging and in scientific visualization. Scientific visualization of the scalar data is the representation of data graphically as a means of understanding and to have an clear insight into scientific data. Scientific visualization helps to automate the process, minimize human intervention, understand the spatio temporal nature of the huge data and for real time visualization. The scalar data is visualised based on its Isosurfaces or Level sets. In this project our goal is two fold - firstly, to study the algorithm for visualising the Isosurfaces of a scalar field and secondly, to understand the topological evolution of the Isosurfaces corresponding to the range of the scalar data. To understand the formation of contours at a particular isolevel in a scalar field we have used Marching Cubes algorithm. The algorithm used for the construction of Iso surfaces from the given volumetric data is called "marching cubes" algorithm. Then we study a contour tree algorithm that is a data structure for capturing the level set topolgy of a scalar field. The Contour Tree can be used to build the user interfaces reporting the complete topological characterization of a scalar field. Data exploration time can be reduced as the user understands the evolution of level set components by changing isovalue. The augmented Contour Tree (CT) provides more accurate information segmenting range space of a scalar field in the portion of an invariant topology. The exploration time of a single Isosurface is improved as its genus is known well in advance. A simple Contour Tree (CT) implementation algorithm was used for constructing the contour tree for a scalar field. The algorithm is divided into three stages: sorting of the vertices in the field, computing the Join Tree (JT) and Split Tree (ST), and merging the JT with the ST to build the Contour Tree.

Keywords: Isovalues, Isolines, Isosurfaces, Level Sets, Join tree, Spilt tree.